$A$ car moving with a velocity of $10 \, m/s$ can be stopped by the application of a constant force $F$ in a distance of $20 \, m$. If the velocity of the car is $30 \, m/s$,it can be stopped by this same force in what distance (in $, m$)?

$A$ particle $(m = 1 \; kg)$ slides down a frictionless track $(AOC)$ starting from rest at a point $A$ (height $2 \; m$). After reaching $C$,the particle continues to move freely in air as a projectile. When it reaches its highest point $P$ (height $1 \; m$),the kinetic energy of the particle (in $J$) is: (Figure drawn is schematic and not to scale; take $g = 10 \; ms^{-2}$)

$A$ car accelerates from rest to $u \ m/s$. The energy spent in this process is $E \ J$. The energy required to accelerate the car from $u \ m/s$ to $2u \ m/s$ is $nE \ J$. The value of $n$ is ..............

$A$ body of mass $2 \, kg$ is projected vertically upwards with a velocity of $2 \, m/s$. The kinetic energy $(K.E.)$ of the body just before striking the ground is ............. $J$.

$A$ knife of mass $m$ is at a height $x$ from a large wooden block. The knife is allowed to fall freely,strikes the block and comes to rest after penetrating distance $y$. The work done by the wooden block to stop the knife is ..............

Write the equation of total mechanical energy of a body of mass $m$ falling freely from a height $H$.